For tangentially elastic belt constructions of vehicle tires strip-shaped strengtheners are known as so-called transverse belts, which can be pre-shaped radially in a number of planes (EP 0 357 826). These sinusoidal or similarly wavy strips of the transverse belt are, it is true, in a position to perform the desired longitudinal stretching, but they are frequently subject to tears or similar damage on added local deformations of the belts in a radial and lateral direction. Moreover the known wavy strips of the transverse belt take up a relatively large amount of space as they have to be covered over by the rubber matrix over the height of the amplitudes of the waves for mechanical and manufacturing reasons. This has the consequence of involving a relatively large volume of the belt which both adds to cost and also wastes unnecessary energy through internal friction in the body of the belt.